<h3>
<u>Answer:</u></h3>
<h3>
<u>Step-by-step explanation:</u></h3>
A inequality is given to us and we need to convert it into standard form and see whether if it has a solution . So let's solve the inequality.
The inequality given to us is :-
Let's plot a graph to see its interval . Graph attached in attachment .
Now we can see that the Interval notation of would be ,
![\boxed{\boxed{\orange \tt \purple{\leadsto}y \in [-2,-1] }}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7B%5Corange%20%5Ctt%20%5Cpurple%7B%5Cleadsto%7Dy%20%5Cin%20%5B-2%2C-1%5D%20%7D%7D)
<h3>
<u>Hence</u><u> the</u><u> </u><u>standa</u><u>rd</u><u> </u><u>form</u><u> </u><u>of</u><u> </u><u>inequa</u><u>lity</u><u> </u><u>is</u><u> </u><u>y²</u><u>+</u><u>3y</u><u> </u><u>+</u><u>2</u><u> </u><u>≤</u><u> </u><u>0</u><u> </u><u>and</u><u> </u><u>the </u><u>Solution</u><u> </u><u>set</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>ineq</u><u>uality</u><u> </u><u>is</u><u> </u><u>[</u><u> </u><u>-</u><u>2</u><u> </u><u>,</u><u> </u><u>-</u><u>1</u><u> </u><u>]</u><u> </u><u>.</u></h3>
U = ( -8 , -8)
v = (-1 , 2 )
<span>the magnitude of vector projection of u onto v =
</span><span>dot product of u and v over the magnitude of v = (u . v )/ ll v ll
</span>
<span>ll v ll = √(-1² + 2²) = √5
</span>
u . v = ( -8 , -8) . ( -1 , 2) = -8*-1+2*-8 = -8
∴ <span>(u . v )/ ll v ll = -8/√5</span>
∴ the vector projection of u onto v = [(u . v )/ ll v ll] * [<span>v/ ll v ll]
</span>
<span> = [-8/√5] * (-1,2)/√5 = ( 8/5 , -16/5 )
</span>
The other orthogonal component = u - ( 8/5 , -16/5 )
= (-8 , -8 ) - <span> ( 8/5 , -16/5 ) = (-48/5 , -24/5 )
</span>
So, u <span>as a sum of two orthogonal vectors will be
</span>
u = ( 8/5 , -16/5 ) + <span>(-48/5 , -24/5 )</span>
Answer:
gravitational Potential Energy
Step-by-step explanation:
